import matplotlib.pyplot as plt

import random
import torch
from d2l import torch as d2l

def synthetic_data(w,b,num_examples):
    X=torch.normal(0,1,(num_examples,len(w)))
    y=torch.matmul(X,w)+b
    y+=torch.normal(0,0.01,y.shape)
    return X,y.reshape((-1,1))

true_w = torch.tensor([2,-3.4])
true_b=4.2
features,labels=synthetic_data(true_w,true_b,1000)
print('features:',features[0],'\nlabel:',labels[0])
d2l.set_figsize()
d2l.plt.scatter(features[:,1].detach().numpy(),labels.detach().numpy(),1)

# plt.scatter(features[:,1].detach().numpy(),labels.detach().numpy())
plt.show()

def data_iter(batch_size,features,labels):
    num_examples=len(features)
    indices=list(range(num_examples))
    random.shuffle(indices)
    for i in range(0,num_examples,batch_size):
        batch_indices=torch.tensor(indices[i:min(i+batch_size,num_examples)])
        yield features[batch_indices],labels[batch_indices]

batch_size=10
for X,y in data_iter(batch_size,features,labels):
    print(X,'\n',y)
    break

w=torch.normal(0,0.01,size=(2,1),requires_grad=True)
b=torch.zeros(1,requires_grad=True)

def linreg(X,w,b):
    """线性回归模型"""
    return torch.matmul(X,w)+b

def squared_loss(y_hat,y):
    """均方误差"""
    return (y_hat-y.reshape(y_hat.shape))**2/2

def sgd(params,lr,batch_size):
    """小批量随机梯度下降"""
    with torch.no_grad():
        for param in params:
            param-=lr*param.grad/batch_size
            param.grad.zero_()

lr=0.03
num_epochs=3
net=linreg
loss=squared_loss

for epoch in range(num_epochs):
    for X,y in data_iter(batch_size,features,labels):
        l=loss(net(X,w,b),y)
        #X和y对于一个小批量batch的损失
        #因为l形状是('batch_size',1)，而不是一个标量，l中所有元素被加到一起
        #并以此计算关于['w','b']的梯度
        l.sum().backward()
        sgd([w,b],lr,batch_size)
    with torch.no_grad():
        train_l=loss(net(features,w,b),labels)
        print(f'epoch{epoch+1},loss{float(train_l.mean()):f}')

print(f'w的估计误差：{true_w-w.reshape(true_w.shape)}')
print(f'b的估计误差:{true_b-b}')
